The present invention relates to an optical device, and more particularly to an optical device such as waveguide optical modulators and waveguide optical switches used in high speed optical communications, optical switching networks, optical information processing, image processing and other various optical systems.
The waveguide optical modulators and waveguide optical switches are extremely important for realizing the high speed optical communications, optical switching networks, optical information processing, image processing and other various optical systems.
The waveguide optical modulators may be fabricated on a few kinds of attracted substrates. The studies of the waveguide optical devices have been likely to focus on LiNbO.sub.3 substrate or semiconductor substrates such as GaAs substrate. A low loss strip type optical waveguide may be formed in an upper region of the LiNbO.sub.3 substrate by selective diffusion of titanium into the upper region of the LiNbO.sub.3 substrate.
The most important parameters for the waveguide optical modulators are driving voltage, modulation bandwidth and insertion loss. A low driving voltage, a wide bandwidth and a low insertion loss are desired. Notwithstanding, the driving voltage and the modulation bandwidth have a relationship of trade-off each other. Namely, it was difficult to satisfy the requirements for reduction in the driving voltage and widening the bandwidth concurrently. In this circumstances, the studies of the waveguide optical modulators have been focusing on the optimization of the trade-off relationship between the driving voltage and the bandwidth.
It had been known in the technical field to which the invention pertains that the bandwidth of the waveguide optical modulators mainly depends upon the kind, material and placement of the electrode and a dielectric constant of the substrate. A traveling wave electrode is useful for wide band modulation. The traveling wave electrode is configured as an extension from a driving power transmission line, for which reason a characteristic impedance of the traveling wave electrode is required to be equal to a characteristic impedance of a power supply or a cable. In this case, a modulation speed is defined by a difference in traveling time, phase velocity or effective refractive index between optical wave and microwave. Useable traveling wave electrodes are asymmetric strip line type electrode, asymmetric coplanar strip type electrode, and coplanar waveguide type electrode.
A conventional Mach-Zehnder optical modulator as one of the typical optical modulators is illustrated in FIGS. 1, 2 and 3. FIG. 1 is a plane view illustrative of the first conventional Mach-Zehnder optical modulator including a dielectric buffer layer having a constant thickness. FIG. 2 is a cross sectional elevation view illustrative of the first conventional Mach-Zehnder optical modulator of FIG. 1. FIG. 3 is a schematic perspective view illustrative of the first conventional Mach-Zehnder optical modulator of FIGS. 1 and 2.
A crystal substrate 1, for example, a LiNbO.sub.3 substrate is used. A titanium film strip is formed on a top surface of the crystal substrate 1, wherein the titanium film strip comprises two straight arms and two Y-shaped portions coupled to opposite sides of the two straight arms. The crystal substrate 1 was then subjected to a heat treatment at a temperature in the range of 900.degree. C. to 1000.degree. C. for 5-12 hours to cause a diffusion of titanium in the titanium film strip into an upper region of the crystal substrate 1 to form a titanium-diffused optical waveguide in the upper region of the crystal substrate 1. The titanium-diffused optical waveguide comprises a Y-shaped optical divider portion 2, two straight arm phase shifter portions 4 coupled to the Y-shaped optical divider portion 2, and a Y-shaped optical coupler portion 3 coupled to the two straight arm phase shifter portions 4. Optical fiber mounts 9 are provided at opposite end portions of the titanium-diffused optical waveguide so that the Y-shaped optical divider portion 2 and the Y-shaped optical coupler portion 3 ate coupled via the optical fiber mounts 9 to optical fibers. The top surface of the titanium-diffused optical waveguide has the same level as the top surface of the crystal substrate 1 to form a flat surface. A dielectric buffer layer 5, for example, SiO.sub.2 buffer layer is provided entirely on the flat surface so that the dielectric buffer layer 5 extends over the optical waveguide and the crystal substrate 1. The dielectric buffer layer 5 has a constant thickness.
A coplanar waveguide type electrode is selectively provided on the dielectric buffer layer 5. The coplanar waveguide type electrode structure comprises a signal electrode 6 and two ground electrodes 7.
Here, a first one of the two straight arm phase shifter portions 4 is defined as having a larger value on the X-coordinate, while a second one of the two straight arm phase shifter portions 4 is defined as having a smaller value on the X-coordinate.
The signal electrode 6 extends in the Y-direction and over the dielectric buffer layer 5 over the first one of the two straight arm phase shifter portions 4 so that the signal electrode 6 entirely covers in the plane view the first one of the two straight arm phase shifter portions 4. The signal electrode 6 further extends in the X-direction toward the lower position on the X-coordinate and over the Y-shaped optical divider portion 2 and the Y-shaped optical coupler portion 3 so that the signal electrode 6 is coupled with connector packages 8 at the lower position on the X-coordinate than the position of the second one of the two straight arm phase shifter portions 4. A first one of the two ground electrodes 7 extends over the dielectric buffer layer 5 over the second one of the two straight arm phase shifter portions 4 so that the first one of the two ground electrodes 7 entirely covers in the plane view the second one of the two straight arm phase shifter portions 4. The first one of the two ground electrodes 7 further extends over the dielectric buffer layer 5 over the crystal substrate 1 on lower regions on the X-coordinate than and outside the second one of the two straight arm phase shifter portions 4. The first one of the two ground electrodes 7 is separated in the plane view from the signal electrode 6. A second one of the two ground electrodes 7 extends over the dielectric buffer layer 5 so that the second one of the two ground electrodes 7 is positioned outside the signal electrode 6 but separated in the plane view from the signal electrode 6.
A microwave is applied through the connector package 8 to the signal electrode 6. If no phase shift is provided between the two straight arm phase shifter portions 4, then optical waves having been traveled through the two straight arm phase shifter portions 4 have the same phase as each other. For which reason, when the optical waves with the same phase are then coupled by the optical coupler 3, the intensity of optical wave to be output from the modulator remains unchanged from that of the incident optical wave.
If a high voltage is applied to the signal electrode 6, a phase shift at .pi. is provided between the two straight arm phase shifter portions 4 whereby optical waves having been traveled through the two straight arm phase shifter portions 4 have a difference in phase by .pi. from each other. For which reason, when the optical waves with the same phase are then coupled by the optical coupler 3, an offset interference is raised between the coupled optical waves whereby the intensity of the coupled optical wave is zero or almost zero as the minimum value. The optical modulator shows ON-OFF operations as described above.
A second conventional Mach-Zehnder optical modulator with asymmetric strip line type electrodes is illustrated in FIGS. 4 and 5. Except for the electrodes, the structure of the Mach-Zehnder optical modulator is substantially the same as described above with reference to FIGS. 1, 2 and 3.
A third conventional Mach-Zehnder optical modulator with asymmetric coplanar strip type electrodes is illustrated in FIGS. 6 and 7. Except for the electrodes, the structure of the Mach-Zehnder optical modulator is substantially the same as described above with reference to FIGS. 1, 2 and 3.
A fourth conventional Mach-Zehnder optical modulator with asymmetric coplanar waveguide type electrodes is illustrated in FIGS. 8 and 9. Except for the electrodes, the structure of the Mach-Zehnder optical modulator is substantially the same as described above with reference to FIGS. 1, 2 and 3.
As described above, the driving voltage and the modulation bandwidth have a relationship of trade-off each other. The bandwidth of the waveguide optical modulators mainly depends upon the kind, material and placement of the electrode and a dielectric constant of the substrate. On the other hand, the driving voltage mainly depends upon an overlap integral of electric wave, for example, microwave and optical wave, more accurately an overlap integral of a profile of the electric field and an optical mode field profile. As the overlap integral is decreased, then the driving voltage is increased. As the overlap integral is increased, then the driving voltage is decreased. Further, as the thickness of the dielectric buffer layer is increased, the overlap integral is decreased. As the thickness of the dielectric buffer layer is decreased, the overlap integral is increased. Consequently, if the thickness of the dielectric buffer layer is increased, then the driving voltage is also increased. If the thickness of the dielectric buffer layer is decreased, then the driving voltage is also decreased. In the light of reduction in driving voltage, it is preferable to reduce the thickness of the dielectric buffer layer.
1. Driving Voltage
Here, the relationship of the driving voltage to the overlap integral of the electric field profile and the optical mode field profile will be highlighted.
The electrode is provided over the dielectric buffer layer extending over the optical waveguide so that an electric field is applied by the electrode through the dielectric buffer layer to the optical waveguide whereby a profile of refractive index of the optical waveguide is varied in proportion to the intensity of the applied electric field due to linear electro-optic effect so called "Pockels effect". The variation in refractive index of the optical waveguide causes a electro-optic phase shift thereby causing phase modulation.
The refractive index variation .DELTA.n electro-optically caused can be represented as a function of an applied voltage V as follows. ##EQU1## where "n.sub.e " is the abnormal refractive index of the crystal substrate, "r.sub.33 " is the electro-optic constant, "E(x,y)" is the electric field applied to the optical waveguide, "V" is the voltage applied to the electrode, "G" is the gap between the signal and ground electrodes, and ".GAMMA." is the overlap integral of the electric field profile anal the optical mode field profile.
The value of the overlap integral depends upon the distance between the signal and ground electrodes, the electric field profile, the optical mode field profile and the thickness of the dielectric buffer layer. The overlap integral ".GAMMA." is theoretically in the range of 0-1 and given by the following equation. ##EQU2## where .PHI..sup.2 (x,y) is the two-dimensional optical field, E(x,y) is the two-dimensional electric field. The optical field is different from the applied electric field, for which reason the overlap integral represents an overlap amount between the optical field and the applied electric field.
In order to reduce the driving voltage to be applied to the electrode, it is required to increase the overlap integral ".GAMMA." as closely to the theoretical maximum value 1 as possible. Notwithstanding, in prior art, the actually obtainable overlap integral ".GAMMA." is in the range of 0.3-0.6 in consideration of various parameters such as the thickness of the dielectric buffer layer, the width of the signal electrode and the distance between the signal and ground electrodes.
A total amount of the phase shift ".DELTA..beta." caused at the length "L" of the interaction or the electrode is given by the following equation. EQU .DELTA..beta.L=2 .pi.n.sub.e.sup.3 r.sub.33 V.GAMMA.L/.lambda.G(3)
where "n.sub.e " is the abnormal refractive index of the crystal substrate, "r.sub.33 " is the electro-optic constant, "V" is the voltage applied to the electrode, "G" is the gap between the signal and ground electrodes, and ".GAMMA." is the overlap integral of the electric field profile and the optical mode field profile, ".lambda." is the operating wavelength, and "G" is the gap between the signal and ground electrodes.
The switching operations or ON-OFF operations are obtainable by shifting the phase by zero and .pi. radian. If the applied voltage is zero, then no phase shift is caused whereby the optical modulator or optical switch is placed in the ON-state. If the applied voltage is a predetermined value, then a phase shift by .pi. radian is caused whereby the optical modulator is placed in the OFF-state.
In the equation (3), the .DELTA..beta.L is replaced by .pi. before the equation (3) is transformed into the following equation which represents the product of the voltage and the length of interaction or electrode. EQU V.sub..pi. L=.lambda.G/{2n.sub.e.sup.3 r.sub.33 .GAMMA. (4)
where V.sub..pi. is the applied voltage causing the phase shift by .pi. radian, namely so called "switching voltage". From the above, the overlap integral .GAMMA. and the switching voltage V.sub..pi. can be calculated as follows. First, the refractive index profile of the optical waveguide is calculated. Second, the optical field profile is calculated by a specific mode calculation. Further, the profile of the applied electric field is also calculated. The overlap integration ".GAMMA." can be calculated from the equation (2) and the switching voltage "V.sub..pi. L" or "VL" can be calculated from the equation (4).
2. Frequency Response and Bandwidth
Frequency response and bandwidth of the traveling wave modulator will be considered. The intensity of the output is determined by the total shift amount of the phase of the traveling wave. The total shift amount of the phase of the traveling wave is given by the following equation. EQU .DELTA..PHI.(t)=.DELTA..PHI..sub.1 (t)-.DELTA..PHI..sub.2 (t)(5)
where .DELTA..PHI..sub.1 (t) and .DELTA..PHI..sub.2 (t) are respective phase shifts of the first and second arm phase shifter portions of the optical waveguide.
The phase shift .DELTA..PHI.(t) is also given by the following equation. EQU .DELTA..PHI.(t)={Z/(Z.sub.S +Z)}(.pi./.lambda.)V.sub.g cos (2 .pi. ft)Lr.sub.33 n.sub.e.sup.3 .GAMMA.H(f) (6)
where "Z" is the impedance of the optical modulator, "Z.sub.S " is the impedance of the light source, "L" is the length of the electrode, "V.sub.g cos(2 .pi. ft)" is the microwave generation voltage, ".lambda." is the free space optical wavelength, "n.sub.e " is the abnormal refractive index of the crystal substrate, "r.sub.33 " is the electro-optic constant, ".GAMMA." is the overlap integral and H(f) is the frequency response function.
The frequency response function H(f) can be derived from the total phase shift depending upon the frequency which is caused by the applied microwave voltage. The frequency response function H(f) is given by the following equation. ##EQU3## where "u" and ".alpha." are respectively given by the following equations. EQU u=.pi.fL(n.sub.m -n.sub.o)/C (8)
where "f" is the frequency, "L" is the length of the interaction or electrode, "n.sub.m " is the refractive index of microwave, "n.sub.o " is the is the refractive index of optical wave and "C" is the light velocity. EQU .alpha.=.alpha..sub.0 (f).sup.1/2 (9)
where ".alpha." is the microwave attenuation and ".alpha..sub.0 " is the microwave attenuation constant.
The small signal relative frequency response .PHI.(f)/.PHI.(f=0)" is given by H(f) in the equation (7).
The bandwidth can be found lay solving H(f)=1/.sqroot. 2. If there is no loss, H(f) can be transformed into sine function and the bandwidth is given by the following equation. EQU Bandwidth=1.4C/[.pi.L(n.sub.m -n.sub.o)] (10)
However, the bandwidth is generally defined by the microwave attenuation ".alpha." and the velocity mismatch "(n.sub.m -n.sub.o)". In order to reduce the velocity mismatch "(n.sub.m -n.sub.o)", it is required to optimize parameters of the dielectric buffer layer and parameters of the electrodes, particularly the width of the signal electrode and the gap between the signal and ground electrodes.
One of the results of optimizations to the parameters of the dielectric buffer layer and the electrodes is disclosed in IEEE Photonics Technology Letters, Vol. 4, No. 9, September 1992 entitled "A Wide-Band Ti:LiNbO.sub.3 Optical Modulator with a Conventional Coplanar Waveguide Type Electrode". A bandwidth of 20 GHz and a driving voltage of 5V were obtained, where the length of electrode is 2.5 cm. A reduction in driving voltage from 5V to 3V was dried by increase in the length of the electrode from 2.5 cm to 4 cm, whilst the bandwidth is narrowed. In order to widen the bandwidth without dropping the driving voltage, it is required to reduce the microwave attenuation.
3. Microwave Attenuation
Microwave attenuation is caused by the following events:
a) Loss of strip line conductance which is a function of placement of electrode, resistivity of electrode material and parameters of dielectric buffer layer; PA1 b) Dielectric loss which is a function of dielectric constant of LiNbO.sub.3 substrate and a loss tangent "tan .delta."; PA1 c) Loss due to higher mode propagation; PA1 d) Loss due to curvature or tapering of the strip line; PA1 e) Loss due to impedance mismatch between 50.OMEGA. light source and load; and PA1 f) Loss due to mounting package and outside package which includes loss due to connector and connector strip line contact.
If the velocity matching and the reduction in the microwave attenuation as well as the characteristic impedance near 50.OMEGA. could be tried to be obtained by optimizing the thickness of the buffer layer, the thickness and width of the signal electrode, the gap between the signal and ground electrode. As a result, the driving voltage is fixed. In order to obtain a further reduction in the driving voltage, it is required to reduce the thickness of the dielectric buffer layer. However, as described above, the reduction in the thickness of the dielectric buffer layer for the purpose of the reduction in the driving voltage causes the bandwidth to be narrowed and characteristic impedance to be apart from 50 .OMEGA..
In the above circumstances, it had been required to develop a novel waveguide optical device with a wide bandwidth, a low driving voltage and a low microwave attenuation.